For CPUs, they generally do a finite amount of work at once and then go back to idle. What do GPUs do? if a GPU can pump out 200FPS, will it realize that that is wayyyy too much for a 60Hz monitor and run at a lower clock rate?

No they don't, the GPU's usage will vary depending on load. You can easily check for this using some diagnostics software such as AIDA64 among others under GPU usage. It would be VERY unpractical if a GPU ran at 100% at all times, imagine the heat.